Task
3
End of Las Vegas?
Topic
Proportional Relationships,
Lines & Linear Equations
Common Core State Standards
8EE5
Copyright @ 2016 The Regents of the University of California
This work was supported by grant number #DRL-1020393 from the National Science Foundation
and grant number 2012-8075 from the William and Flora Hewlett Foundation.
Agenda
Set Up
Whole class, 5 min
Mind Stretch
Whole class, 5 min
Workout
Check Your Pulse
Final Lift
Individual, 10-15 min
Pairs, Individual, Whole class, 10 min
Individual, 15 min
How can we use
math to think
about big
problems in our
world?
Setup
Learning Goals & Expectations
We are
learning to…
Make connections between representations of
the same rate.
Compare and contrast different rates.
Identify where slope changes within a graph.
We will be
successful
when we…
Connect equations, figures and graphs that
represent the same rate.
Explain how an equation, figure, and graph
are related to one another.
Interpret a graph, describing the slope and any
change of slope.
High Quality Work
Work is
accurate &
precise
Explanations
Problem is set up in a way that helps you solve it.
Scale: responses use appropriate units.
Work has been checked for calculation errors.
Describe what you did and why you did it.
Use multiple representations to show your
thinking about math.
Include a logical argument and evidence to
support each answer. It makes sense.
Multiple Representations
Use multiple representations to help you think and to
show your thinking to others.
Representations
Create a chart or table
Set up an equation or an algebraic rule
Sketch a graph
Use words to explain and justify
Prior Knowledge
Earned Run Average
More mouths to feed
Currency Exchange
Fill ‘er up
“When will we get there?”
Mind Stretch
The story so far…
Nevada and California are in the middle of a
drought. Unless something changes, Las Vegas
may soon run out of water. The lake that supplies
90% of the water for Las Vegas, Lake Mead, will
be at a level so low by 2021 that it will not provide
any water.
Lake Mead Water Levels
Mind Stretch
An average shower uses 5 gallons
of water per minute.
1. About how many minutes do you spend showering
each day?
2. Show how you would estimate the number of
gallons of water you use showering for this many
minutes each day.
3. Show how you would estimate the number of
gallons of water you use showering in one week (7
days)?
4. Write an equation showing how many gallons of
water you use showering in x days. Use the
variable y to represent the gallons of water used.
Workout
Workout
Facts:
•
•
•
Las Vegas uses water at a rate of 219 gallons per person per day.
Los Angeles uses water at a rate of 123 gallons per person per day.
San Francisco uses water at a rate of 49 gallons per person per day.
1.
Sketch a line to represent each city’s water use per person over time on
the same graph.
2.
Explain how use of water per person in Las Vegas, Los Angeles, and
San Francisco compare over time
Workout (cont.)
Researchers calculated how much water each city uses per year
(in acre feet).
Acre foot: unit of volume. An area of one acre filled to a depth of
one foot. 1 acre foot = 325,851 gallons
They created graphs, equations, and pictures to represent how
each city’s water storage declines with every day of water use.
Take out your End of Vegas cards to complete the workout. Match
the graph, equation and picture cards for each city.
3. Attach the graph, equation and picture card for Los Angeles
to your worksheet.
Explain how you know these are the correct representations for
the water use in Los Angeles. In your answer, please explain
what specific information from each representation connects it
to the water use in Los Angeles.
Check
Your Pulse
Check Your Pulse
Compare your answers with
a partner. Then discuss…
•
Where do you agree or disagree with your partner’s answer?
•
What part(s) were difficult for you?
Check Your Pulse
On your own… self-assess:
1. Circle your level of understanding for the Workout.
I have lots of
questions. I need help
Almost got it, but I
need practice
Got it.
Ready to move on.
Final Lift
Final Lift
During the drought each household gets a water
“allowance” of 200 gallons per day. This is a graph
of how a family used water from 6am to 6pm on a
How much water is left?
Saturday.
B
Final Lift
1. Label the graph at points where the slope changes.
2. Based on the graph, describe how the slope changes at
each point and what might be happening.
3. Which of the given equations fits segment drawn
between 6:00 AM and 8:00 AM?
4. Does the answer you circled above suggest a
proportional relationship between x and y? Explain.
Final Lift (Continued)
5. Does the slope of the line on the graph change, or is it
constant, between 6:00 AM and 6:00 PM? Explain your
thinking.
6. If the family cuts their water use in half between 6 AM
and 8 AM, how would the line on the graph change? As
part of your answer, explain why you think this.
7. If the family cuts their water use in half between 6 AM
and 8 AM, how would the equation you selected
change? As part of your answer, explain why you think
this.
Challenge
The mayor of LA challenges the mayor of Las
Vegas, saying, “We will reduce our water use more
than you.” Las Vegas’ mayor accepts the challenge.
During the next year:
•LA cuts water use from 123 gallons to 61 gallons per person
per day.
•Las Vegas cuts water use from 219 to 139 gallons per person
per day.
Los Angeles has about 15 million residents; Las
Vegas has about 2 million residents.
Who cut their water use more? Explain your
reasoning.